Question

2) I am about to choose an integer, at random, from amongst the following positive integers: {1,2,3,4, …., 25, 26, 27}

a) is this an example of discrete or continuous uniform probability distribution? Please explain

b) what is the probability that I coincidentally happen to choose integer “23”? show work

c) please depict this probability distribution in some appropriate manner.

d) please determine the probability that I choose: either an even integer, or an integer which is at least 20? Recall: PROB(A or B)+PROB(B)-PROB(A&B). show work

e) please determine the mean value for this probability function. Show work

f) please determine the standard deviation for this probability function. Show work

Answer 1

a)

This is an example of a discrete uniform probability distribution. Because here let X be a random variable representing the chosen integer from the set {1,2,3,...............,26,27}

Then X can be =1,2,3,................,27 These are isolated values. So X is a discrete random variable here and X has discrete distribution.

b)

Since all the integers here are equally likely to be chosen, the probability of choosing a single integer 23 is =1/27=0.037

c)

The probability mass function of X is given by

d)

Let A= the event that we choose an even integer. and B= the even that we choose an integer which is atleast 20.

Then we need to find

now here even integers are =2,4,6,8,......,26

So

Now integers atleast 20 are 20,21,22,,........,26,27

So,

Now the event that we choose an even integer which is atleast 20 these integers are 20,22,24,26

So =17/27

e)

Mean =

f) standard deviation=

Now

Then variance(X)= So standard deviation=